“On Philosophical Errors in the Works of Academician L. I. Mandelstam”

(Resolution of the Academic Council of the P. N. Lebedev Physical Institute of the Academy of Sciences of the USSR, February 9, 1953)

Academician L. I. Mandelstam has outstanding merits in the development of Soviet physics, in the creation of a school, and in the training of scientific personnel. In his scientific investigations in special fields of physics—optics, statistical physics, and radiophysics—L. I. Mandelstam appears as a spontaneous materialist.

The spontaneously materialist attitudes of L. I. Mandelstam also find some reflection in his lectures on the theory of relativity and quantum mechanics.

In the lectures there are repeated appeals to nature, to the objective world. Thus, for example, on p. 230*) we read: “... here an assertion is made concerning the relation between two definite rods. Either it exists in nature, or it does not exist. One may assert that it does not exist; but if it exists, then it is real.”

However, in his scientific work L. I. Mandelstam did not pass from spontaneous materialism to dialectical materialism. Not relying on the only correct scientific worldview, L. I. Mandelstam allowed in his works a number of philosophical errors of a subjective-idealist character, which are contained chiefly in Volume V of the complete collected works—in the posthumously published lectures on the physical foundations of the theory of relativity, delivered in 1933–1934, and in the lectures on the foundations of quantum mechanics, delivered in 1939.

In the lectures on the theory of relativity, Academician L. I. Mandelstam indicated that he tried to avoid a philosophical formulation of questions, and in the last lecture says: “I especially tried to emphasize (I think that this is my wish and my very own opinion—you clearly

*) References without indication of volume refer to Volume V.

assimilated that all questions connected with the theory of relativity are, above all, physical questions. Its philosophical significance is a special question; we, however, were interested in its physical significance” (p. 303).

It is true that the theory of relativity is a branch of physics, not philosophy. But it is obvious that the content of the theory of relativity—questions of space, time, and motion—is closely connected with general philosophical problems. Physics, and in particular the theory of relativity, cannot be presented apart from its connection with philosophy. Such a connection, naturally, is also present in the lectures of L. I. Mandelstam.

Among the philosophical questions touched upon in the lectures, much attention is given to the question of definitions in physics, “of the structure of the concepts with which the physicist works” (p. 177). “In general, in logic, to define a concept,” we read on p. 177, “means to reduce a complex concept to a simpler one, i.e. to one already known (I do not know whether this can be carried through to the end). The physicist, however, requires something different: present a real thing. Only in this way will you connect your concept with the real world.” The spontaneously materialist recognition of the real world is combined in this assertion with a number of philosophical errors. It is known that in logic “to define a concept” means to subsume the given concept under another, broader one, and not to “reduce a complex concept to a simpler one.” Thus, for example, we define that heat is a form of energy and thereby subsume the concept “heat” under the broader concept “energy.” The concepts of logic must not be counterposed to the concepts with which physics operates. Every concept is a generalization, an abstraction. Scientific concepts reflect the real world, and an indication only of the connection between individual things and concepts is far from sufficient.

In a number of lectures, Academician L. I. Mandelstam consistently advances the Machist point of view on the essence and role of concepts and definitions in physics. Thus, on p. 180 we read: “A whole series of concepts is not cognized, but is defined for the cognition of nature” (emphasized in the lectures).

It is known that scientific abstractions and definitions are the result of the generalization of accumulated knowledge.

It is obvious that, in studying the phenomena of nature, we cognize not our concepts, but the world around us, objectively existing independently of the concepts we establish. The concepts themselves are established on the basis of accumulated knowledge, and therefore the assertion that “a whole series of concepts is not cognized, but is defined for the cognition of nature” is erroneous.

L. I. Mandelstam often identifies the measurement of physical quantities with their definition. Thus, for example, on p. 183 we read: “... we define time with the aid of some physical process, for example, the rotation of the earth,” or on p. 185: “Let us take

for simplicity, the definition of time by a chronometer. Thus time, i.e., what is substituted into Newton’s formulas in place of $t$, is what the hand of my clock shows.” From the fact that time is measured with the aid of some periodic process, it by no means follows that time “is what the hand of my clock shows.” Such an identification of time with the indication of a clock is Machist in its very essence and reduces the scientific problem of studying time, as a form of the existence of matter, to the establishment of certain “recipes” for measurement. On the question of measurements in general and, in particular, for example, of length, L. I. Mandelstam asserts: “The physicist must have a ‘recipe’ for how to find length. He must indicate such a recipe; he does not discover it, but defines it” (p. 178).

“Nature,” L. I. Mandelstam believes, “does not impose definitions unambiguously, but neither does it allow just any definitions to be given. More precisely, it does allow them, but if I define quite arbitrarily, then I shall be unable to do anything further” (p. 179). These assertions are erroneous, since the laws of nature exist objectively, independently of consciousness and definitions, and in science definitions cannot be arbitrary; they reflect that which exists objectively.

L. I. Mandelstam connects the definitions of physical quantities only with recipes for measurements. Such a solution of the question, in which science deals only with the results of measurements, leads to agnosticism and idealism. It is perfectly obvious that measurements are a means by which phenomena of nature and regularities, objectively existing independently of people—in particular, of physicists and of the measurements they carry out—are studied.

Spatio-temporal relations exist independently of our measurements and prior to any measurements. Therefore such assertions as: “I ... have not learned what length is, but I have defined what I will call length,” or “the concept of simultaneity is a matter of definition” (p. 190), are profoundly erroneous and, as is well known, are used abroad and personally by Einstein for the propaganda of Machism. So long as there were no people, and before the time when they learned to distinguish space and time, naturally there were no such concepts as length, simultaneity, and so on. But spatio-temporal relations existed and exist independently of our definitions. Such concepts as length, simultaneity, and so on, reflect that which exists objectively in nature.

It is incorrect to assert, as is done in the lectures, that “the concept of simultaneity is a matter of definition.” The development of physics has shown that simultaneity is not absolute, as classical physics maintained, proceeding from metaphysical conceptions of space and time. However, the simultaneity of events exists independently of our definitions. Classi-

classical physics held that time is not connected with matter and motion, and assumed, in particular, that the simultaneity of events does not depend on the motion of material objects. The theory of relativity showed that time and space are connected with the motion of matter, and specifically confirmed the proposition of dialectical materialism, expressed long before the appearance of the theory of relativity, that time and space are forms of the existence of matter.

The theory of relativity revealed that the simultaneity of events is not absolute, but depends on the motion of material objects. Our knowledge of time and space became more exact, but it in no way follows from this that simultaneity is a matter of definition and not the reflection of an objective property of space-time relations.

In examining the question of establishing units of length (standards) in systems moving relative to one another, L. I. Mandelstam reduces this problem to the establishment of a “common language” and says: “We must choose such a language that the standard, measured from one system and from another, will be the same” (p. 223), or: “The principle of relativity asserts or presupposes something greater—that I can choose a language in which phenomena in another system would be described in the same way as in the first” (p. 212).

Statements of this kind, in which the establishment of the objective properties of phenomena is reduced to a “choice of language,” likewise show L. I. Mandelstam’s erroneous philosophical views on the essence and role of physics, since the laws of nature do not depend on one or another agreement among scientists.

When L. I. Mandelstam raises questions of the theory of knowledge, he resolves these philosophical questions incorrectly, just as the foreign physicist-Machists do. Thus, for example, on the question of the role of theory, following Poincaré, L. I. Mandelstam believes that “separate experimental data, separate phenomena—these are the volumes of which the library consists. Theory is the catalogue of the complete library” (vol. III, p. 354). It is not hard to see that Poincaré, in identifying theory with a catalogue, proceeds from the Machist “principle of economy of thought.” In reality, as we know, theory is a generalization of experimental data verified by practice. Theory reflects laws that exist objectively in nature. A catalogue, however, is an arbitrary systematization carried out for convenience of use.

The statement cited dates from 1918, but on this question L. I. Mandelstam’s point of view did not change in subsequent years.

Thus, in an addition to his lectures on the foundations of quantum mechanics, L. I. Mandelstam poses the question—“To what extent do they differ, and do dif-

whether there exist, in general, common principles of construction for quantum theory from those principles of a theoretical-cognitive character which lay at the foundation of the physical theories of the classical period” (Vol. V, p. 407). In this connection L. I. Mandelstam writes: “Every physical theory can be divided into the following stages.

First of all, the theory introduces, depending on one or another domain of physical phenomena to which it pertains, certain mathematical quantities. For example, in mechanics such quantities are coordinates, velocity, time, etc.; in the theory of heat—temperature, quantity of heat, entropy, and so on; in electrodynamics—the electric and magnetic fields. Mathematical relations are established between these quantities, for example in the form of differential equations: Newton’s mechanical equations, Maxwell’s electrical equations. This stage, which sometimes by itself bears the name of a physical theory, is by no means such, since in general it contains no statements relating to physical phenomena.

The second stage consists in correlating mathematical quantities with physical objects. This is achieved by giving, for each quantity, a definite recipe indicating by what procedure we can assign to the given physical object one or another numerical value of this quantity. We call this the recipe for measuring the given physical quantity. Finally, these same recipes serve for the reverse transition from the new values of the quantities, obtained from the first by means of the formal mathematical apparatus indicated above, back to physical objects.

An example will best clarify what has been said. We measure, for instance, the position of a planet at a given moment of time. The recipe is as follows: we count off the corresponding divisions of the limb of the telescope when the intersection of the ocular threads coincides with the given planet, and at the same time the position of the hands of the clock, i.e. we determine the value of the angular coordinates at the given moment of time. Then we substitute the numbers thus obtained into the corresponding equations as initial conditions. The equations give us new joint values of the coordinates and time \((t, \varphi, \psi)\). The statement of the theory consists in the assertion that, having set the telescope in accordance with the values of the divisions of the circles obtained from these equations, we shall see the planet at the intersection of the threads simultaneously with the passage of the clock hand through the number on the dial equal to \(t\).

Only the totality of all the indicated stages constitutes the theory” (Vol. V, p. 408).

The reasoning and example cited are typical in their tendency to restrict physics as a science to what pertains only to the results of measurements. This is a general feature characterizing all idealistic statements on questions of physics.

It is not the objective world and its regularities that are the object of study, but the readings of instruments.

It is true that without measurements and instruments one cannot do physics, but it is still clearer that instruments and measurements are auxiliary means for investigating phenomena and laws that exist objectively and independently of instruments and measurement prescriptions.

If the data of science relate only to the results of measurements, to observations, then the object of science is not the objective world but “complexes of sensations,” and such assertions are only a repetition of idealist Machist statements.

The philosophical errors that were committed by L. I. Mandelstam were also committed in their time by some of his pupils and found dissemination in individual physics textbooks, such as, for example, Mechanics by S. E. Khaikin, A Course of Physics, Vol. II, edited by N. D. Papaleksi.

The lectures of L. I. Mandelstam included in Volume V of his works were published posthumously from listeners’ notes and are not a work prepared by the author for publication. The commission for the publication of the works of L. I. Mandelstam, having assumed responsibility for publishing lectures not revised by the author, should, in publishing erroneous philosophical statements, have provided its own critical comments on them.